Planar oscillations and dissipative heating of viscoelastic plates with a piezoeffect

Abstract

Planar oscillations of thin piezoplates are important within the context of using this type of piezoelements as resonator frequency filters, frequency stabilizers, elements of piezotransformers, and other technological devices. In the publications currently known one usually considers piezoplates with elastic material behavior and linear governing equations. By their mechanical nature, however, a number of piezoelements, particularly piezoceramics, are viscoelastic, which, depending on the loading conditions, can lead to substantial dissipative heating of the piezoelement and confine its operation [3]. The use of piezopolymers and their composites raises particularly important issues of dissipative heating. At the present time the behavior of a piezoelement including heating can be described by the theory of thermoelectroviscoelasticity (TEVE) [2, 3], including the interaction between electromechanical and thermal fields. The complexity of TEVE problems leads to the necessity of using numerical methods to solve them, with the finite element method (FEM) being widely used in recent years. The present study is devoted to stating and solving TEVE problems concerning thin piezoceramic plates by the FEM. We treat a thin piezoceramic plate, confined by an arbitrary contour L and polarized across its thickness. A harmonic potential difference Δφe^iωt is supplied to electrodes located on the smooth boundaries of the plate. Convective heat exchange with the surrounding media of temperatures T ^s_k and T^s is implemented at the contour surfaces and boundaries free of electrodes. The heat transfer coefficients equal, respectively, α ^T_k and α^T. The initial plate temperature is T₀. The smooth boundary are free of mechanical loading. The mechanical forces at the contour surfaces are distributed symmetrically with respect to the mean plane of the plate.